Name_____________________________
Geometry
Opening Activity
1. Given:
Prove that
2.
,
, and
is a right angle.
Mod 2 Review
bisects
Date___________
Name_____________________________
Geometry
Mod 2 Review
Date___________
Center 1
1. In the xy-coordinate plane, ∆𝐴𝐵𝐶 has vertices 𝐴(−4,6), 𝐵(2,6), and
𝐶(2,2). ∆𝐷𝐸𝐹 is shown in the plane.
What is the scale factor and the center of dilation that maps ∆𝐴𝐵𝐶 to ∆𝐷𝐸𝐹?
(a) The scale factor is 2, and the center of dilation is point B.
(b) The scale factor is 2, and the center of dilation is the origin.
1
(c) The scale factor is 2, and the center of dilation is point B.
1
(d) The scale factor is 2, and the center of dilation is the origin.
2. In the coordinate plane, line p has slope 8 and y-intercept (0,5). Line r is the result of dilating line p by a factor of 3
with center (0,3). What is the slope and y-intercept of line r?
(a) Line r has a slope of 5 and y-intercept (0,2).
(b) Line r has a slope of 8 and y-intercept (0,5).
(c) Line r has a slope of 8 and y-intercept (0,9).
(d) Line r has a slope of 11 and y-intercept (0,8).
3. Line segment AB with endpoints 𝐴(4,16) and 𝐵(20,4) lies in the coordinate plane. The segment will be dilated with a
3
scale factor of and a center at the origin to create ̅̅̅̅̅̅
𝐴′𝐵′. What will be the length of ̅̅̅̅̅̅
𝐴′𝐵′?
4
4. The equation of line h is 2𝑥 + 𝑦 = 1. Line m is the image of line h after a dilation of scale factor 4 with respect to the
origin. What is the equation of the line m?
(a ) 𝑦 = – 2𝑥 + 1
(b) 𝑦 = – 2𝑥 + 4
(c) 𝑦 = 2𝑥 + 4
(d) 𝑦 = − 8𝑥 + 4
5
Name_____________________________
Geometry
Mod 2 Review
Date___________
Center 2
6. Solve for x, y and z
a.
b.
c.
8. A ball is dropped from the top of a 58 ft building. Once the ball is released a strong gust of wind blew the ball off
course and it dropped 10 ft from the base of the building.
Sketch a diagram of the situation.
By approximately how many degrees was the ball blown off course? Round your answer to the nearest whole degree.
Find the missing values ( In not a whole number leave the answers in the simplest radical form
a)
x
z
y
6
98
Name_____________________________
Geometry
Mod 2 Review
Date___________
Homework
1. In isosceles ∆𝑀𝑁𝑃, line segment NO bisects vertex ∠𝑀𝑁𝑃, as shown below. If MP = 16,
find the length of ̅̅̅̅̅
𝑀𝑂 and explain your answer.
2. The figure shows ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹 with side lengths as indicated. What is the value of x?
3. In the diagram below of ∆𝐴𝐵𝐶, ⃡𝑇𝑉 ∥ ̅̅̅̅
𝐵𝐶 , 𝐴𝑇 = 5, 𝑇𝐵 = 7, and 𝐴𝑉 = 10. What is the length
̅̅̅̅ ?
of 𝑉𝐶
4. In right triangle 𝐴𝐵𝐷, 𝐴𝐵 = 53, and altitude 𝐷𝐶 = 14. Find the lengths of 𝐵𝐶 and 𝐴𝐶.
Name_____________________________
Mod 2 Review
Date___________
Geometry
5. A man who is 5 feet 9 inches tall casts a shadow of 8 feet 6 inches. Assuming that the man is standing perpendicular to
the ground, what is the angle of elevation from the end of the shadow to the top of the man’s head, to the nearest tenth
of a degree?
(1) 34.1
(2) 34.5
(3) 42.6
(4) 55.9
1
1
6. The degree measure of an angle in a right triangle is x, and sin 𝑥 = 3. Which of these expressions are also equal to 3?
Select all that apply.
7. In this figure, triangle GHJ is similar to triangle PQR. Which ratio represents tan 𝐻?
8. Mariela is standing in a building and looking out of a window at a tree. The tree is 20 feet away from Mariela.
Mariela’s line of sight to the top of the tree creates a 42° angle of elevation, and her line of sight to the base of the tree
creates a 31° angle of depression. What is the height, in feet, of the tree?
Name_____________________________
Mod 2 Review
Geometry
9. Explain why cos(x) = sin(90 – x) for x such that 0 < x < 90.
Date___________
10. An unmanned aerial vehicle (UAV) is equipped with cameras used to monitor forest fires. The figure represents a
moment in time at which a UAV, at point B, flying at an altitude of 1,000 meters is directly above point D on the forest
floor. Point A represents the location of a small fire on the forest floor.
A. At the moment in time represented by the figure, the angle of depression from the UAV to the fire has ameasure of
30°. What is the distance from the UAV to the fire?
B. What is the distance, to the nearest meter, from the fire to point D?